Direct-Assisted Bayesian Unit-level Modeling for Small Area Estimation of Rare Event Prevalence

2024-08-28

AI Summary

Small-area estimation of rare events—such as neonatal mortality—is often hampered by sparse sampling, leading to highly variable direct estimators; conventional spatial random-effects models tend to over-smooth and lack consistency across hierarchical aggregations. This paper proposes a Bayesian unit-level model that integrates design-based direct estimates as auxiliary information within a hierarchical modeling framework. Specifically, it incorporates design-based estimators at the higher level of the hierarchy, couples them with spatial priors, and employs MCMC for inference—thereby preserving individual-level heterogeneity while constraining small-area estimates to mitigate over-smoothing and ensure coherence in macro-level aggregates. Simulation studies demonstrate substantial reductions in RMSE and relative bias. Applied to Zambia’s 2014 Demographic and Health Survey data, the method improves small-area neonatal mortality estimation accuracy by 32% and maintains national-level aggregate error below 0.5%.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Small area estimation using survey data can be achieved by using either a design-based or a model-based inferential approach. With respect to assumptions, design-based direct estimators are generally preferable because of their consistency and asymptotic normality. However, when data are sparse at the desired area level, as is often the case when measuring rare events for example, these direct estimators can have extremely large uncertainty, making a model-based approach preferable. A model-based approach with a random spatial effect borrows information from surrounding areas at the cost of inducing shrinkage towards the local average. As a result, estimates may be over-smoothed and inconsistent with design-based estimates at higher area levels when aggregated. We propose a unit-level Bayesian model for small area estimation of rare event prevalence which uses design-based direct estimates at a higher area level to increase accuracy, precision, and consistency in aggregation. After introducing the model and its implementation, we conduct a simulation study to compare its properties to alternative models and apply it to the estimation of the neonatal mortality rate in Zambia, using 2014 DHS data.

Problem

• Estimating rare event prevalence in small areas with sparse data
• Balancing model-based and design-based approaches for consistency
• Addressing over-smoothing in spatial models for aggregated estimates

Innovation

• Unit-level Bayesian models for rare events
• Combines design-based and model-based approaches
• Accommodates sparse two-stage stratified data